On the ergodicity of a class of skew products
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Letϕ: [0, 1]→R have continuous derivativeon the closed interval [0, 1], ∫ 0 1 ϕ(x)dx=0, and letα be irrational. Ifϕ(1) ≠ϕ(0), then (x, y) ↦ (x + α, y + ϕ (x)) is ergodic onR/Z ×R.
KeywordsClosed Interval Irrational Number Closed Inter Continue Fraction Expansion Normalize Haar Measure
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